Hedging (Co)Variance Risk with Variance Swaps∗

Abstract In this paper we introduce a new criterion in order to measure the variance and covariance risks in financial markets. In an asset allocation framework with stochastic (co)variances, we consider the possibility to invest also in variance swaps, that are assets which span the volatility as well as the co-volatility risks. We provide explicit solutions for the portfolio optimization problem. We then compare the optimal wealths obtained with and without (co)volatility products leading to the same expected utility. We use the spread between these wealths as a criterion in order to measure the impact of (co)variance risk. Using real data on major indexes and this criterion, we find that the impact of (co)variance risk is huge in the market. This is consistent with the fast development of variance and covariance-based markets.